Research Directions in Distributed Parameter Systems

by Smith, Ralph C.; Demetriou, Michael A.

• ISBN13: 9780898715484
• ISBN10: 0898715482
• Format: Paperback
• Copyright: 2003-11-01
• Publisher: Society for Industrial & Applied

Summary

Research Directions in Distributed Parameter Systems is composed of eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameters systems. Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems, with the ultimate goal of passing along these perspectives to researchers in the field.

Table of Contents

Foreword	xiii
Preface	xvii
Mathematics and Electromagnetic Theory	1	(16)
Richard Albanese
Richard Medina
John Penn
Introduction	1	(1)
Emerging Technologies	2	(1)
Medical Risk and Electromagnetic Fields	2	(6)
Biological Effects and Electromagnetism	8	(4)
Temperature and Tissue Damage	8	(2)
Effects of Stored Energy	10	(2)
Applications	12	(1)
Imaging with Electromagnetic Fields	12	(1)
Therapy	13	(1)
Summary and Conclusion	13	(4)
Bibliography	14	(3)
Nonlinear Distributed Parameter Control Systems with Non-Normal Linearizations: Applications and Approximations	17	(38)
John A. Burns
Introduction	17	(2)
Applications and Approximations	19	(6)
The Role of Good Applications	19	(3)
The Role of Approximation	22	(3)
A Framework for Nonlinear Problems	25	(13)
Burgers' Equation with Distributed Control	25	(3)
The General Framework of Ghidaglia and Temam	28	(2)
Burgers' Equation with Dirichlet Boundary Control	30	(2)
Burgers' Equation with Neumann Boundary Control	32	(2)
Control of a Thermal Convection Loop	34	(4)
Two Model Problems	38	(6)
Example 1: The Lorenz Equation	38	(2)
Example 2: A Simple 2n-D Problem	40	(4)
Conclusions and Suggestions for Future Research	44	(11)
Bibliography	46	(9)
Homogenization and Applications to Material Sciences	55	(40)
Doina Cioranescu
Model Example, Main Homogenization Results	56	(7)
The Classical Methods in Homogenization	63	(5)
The Multiple-Scale Method	63	(2)
Tartar's Oscillating Test Functions Method	65	(2)
The Two-Scale Convergence	67	(1)
The Periodic Unfolding Method	68	(5)
The Periodic Unfolding Operator Tε	68	(1)
Macro-Micro Decomposition of Functions: The Scale-Splitting Operators Qε and Rε	69	(2)
Periodic Unfolding and Homogenization	71	(1)
Corrector Result and Unfolding	72	(1)
Homogenization in Perforated Domains	73	(3)
Homogenization of Truss-Like Structures	76	(10)
The Two-Dimensional Case	77	(5)
Asymptotic Behavior of Grids	82	(3)
Asymptotic Behavior of Truss-Like Beams	85	(1)
Multi-Scale Periodic Unfolding Homogenization	86	(2)
Homogenization of Rubber-Like Materials	88	(7)
Bibliography	93	(2)
Model Reduction for Control Design for Distributed Parameter Systems	95	(28)
Ruth F. Curtain
Introduction	95	(4)
Trotter-Kato Semigroup Approximations	96	(1)
Proper Orthogonal Decomposition Reduced-Order Models	97	(2)
Approximating via Balanced Truncations	99	(4)
LQG-Balancing	103	(5)
Numerical Computation of LQG-Balanced Truncations	108	(4)
Robust Controller Design via LQG-Balanced Truncation	112	(4)
Robust Controller Design via LQG-Balanced Truncation	113	(3)
Conclusions	116	(7)
Bibliography	118	(5)
Max-Plus Linear Partial Differential Equations	123	(16)
Wendell H. Fleming
Introduction	123	(1)
Max-Plus Linearity	124	(1)
Time-Dependent HJB Equations	125	(2)
Vanishing Viscosity, Small Random Perturbations	127	(2)
Max-Plus Fundamental Solutions	129	(1)
Max-Plus Probability and Stochastic Calculus	130	(3)
Max-Plus Basis Expansions	133	(1)
Deterministic Nonlinear Filtering	134	(5)
Bibliography	135	(4)
Geometric Theory of Output Regulation for Linear Distributed Parameter Systems	139	(30)
C. I. Byrnes
D. S. Gilliam
V. I. Shubov
Introduction	140	(2)
Bounded Input-Output	142	(2)
The Regulator Equations and Proof of the Main Theorem	144	(6)
Unbounded Inputs and Outputs	150	(2)
Examples of Regular Linear Systems	152	(3)
Systems with Delays	155	(5)
Tracking and Disturbance Rejection for an Oscillator with Delayed Damping	160	(2)
Future Directions	162	(7)
Bibliography	165	(4)
Smart Structures, Structural Health Monitoring and Crack Detection	169	(18)
Daniel J. Inman
Sergio H. S. Carneiro
Smart Materials and Structures	169	(1)
Structural Health Monitoring	170	(4)
Vibration Suppression	174	(3)
Simultaneous Diagnostics and Control (Level 7)	177	(2)
Self-Healing (Level 6)	179	(1)
Diagnostics of Cracked Beams via Genetic Algorithms (Level 3)	179	(3)
Future Directions	182	(2)
Summary	184	(3)
Bibliography	185	(2)
Survey of Research in Modeling the Human Respiratory and Cardiovascular Systems	187	(32)
F. Kappel
J. J. Batzel
Respiratory System Modeling	188	(6)
Introduction	188	(1)
Survey of Modeling Developments	189	(5)
Current Issues	194	(1)
Models of the Cardiovascular System	194	(7)
Introduction	194	(3)
Survey of Modeling Efforts	197	(3)
Current Issues	200	(1)
Combined Cardiovascular-Respiratory Models	201	(18)
Introduction	201	(2)
A Cardiovascular-Respiratory Model Application	203	(1)
Current Issues	204	(1)
Appendix	205	(1)
Respiratory Model Proposed by Khoo et al	205	(2)
Cardiovascular-Respiratory Model Proposed by Timischl and Kappel 1998	207	(4)
Bibliography	211	(8)
Inverse Problems Related to Electromagnetic Nondestructive Evaluation	219	(18)
Fumio Kojima
Introduction	219	(2)
Parameter Estimation Arising in ECT	221	(6)
Mathematical Model for Inspection Procedures	221	(3)
Mathematical Description of the Observation Mechanism	224	(1)
Inverse Problems and the Associated Parameter Estimation	224	(3)
Inverse Problems for Natural Crack	227	(2)
JSAEM Benchmark Problems	227	(1)
Inverse Analysis by Evolutionary Computation	227	(2)
Open Problems and Current Research Directions	229	(1)
Nondestructive Evaluation of Material Degradation	229	(4)
Characterization of B-H Curve	230	(1)
Stochastic Analysis of the Barkhausen Effect	231	(1)
Structure-Sensitive Magnetic Characterization by Nano-Scale Flaws	232	(1)
Concluding Remarks	233	(4)
Bibliography	233	(4)
Some Suboptimal Strategies for Numerical Realization of Large-Scale Optimal Control Problems	237	(20)
Karl Kunisch
Introduction	237	(1)
A Model Problem	238	(3)
Instantaneous Control-Receding Horizon Control	241	(5)
Reduced-Order Methods	246	(5)
Comments on Suboptimal Closed-Loop Methods	251	(2)
Conclusions	253	(4)
Bibliography	254	(3)
Results and Conjectures for the Control of Navier--Stokes Equations	257	(12)
J. L. Lions
Introduction	258	(2)
The First Two Conjectures Relative to Approximate Controllability	260	(2)
Sensitivity to Reynolds Number	262	(1)
An Attempt to Nonlinear Duality	263	(3)
Further Remarks	266	(3)
Bibliography	267	(2)
Index	269